Finite Group Databasebeta

← #31720513

Subgroups — #31720513

Order 17152.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573765C211yesmaximal, characteristic
2#22569228C211yesmaximal, characteristic, complemented
3#22569227C211yesmaximal, characteristic, complemented
4#22569216C211yesmaximal, characteristic, complemented
5#22569216C212yesmaximal, complemented
6#22569209C212yesmaximal, complemented
7#22569192C212yesmaximal, complemented
8#22569191C212yesmaximal, complemented
9#22569185C211yesmaximal, characteristic, complemented
10#22569181C211yesmaximal, characteristic, complemented
11#22569174C211yesmaximal, characteristic, complemented
12#22569170C211yesmaximal, characteristic, complemented
13#22569157C211yesmaximal, characteristic, complemented
14#22569138C211yesmaximal, characteristic, complemented
15D4×#11761611C211yesmaximal, characteristic, complemented
16#22568935C212yesmaximal, complemented
17#22568909C212yesmaximal, complemented
18#436×D67C211yesmaximal, characteristic, complemented
19#22568870C211yesmaximal, characteristic, complemented
20#22568865C212yesmaximal, complemented
21C4×#14524051C211yesmaximal, characteristic, complemented
22#22568625C212yesmaximal, complemented
23C67×#2969C211yesmaximal, characteristic, complemented
24C2×#14524051C2211yescharacteristic
25C2×#14524051C2211yescharacteristic
26C22×#11761611C2212yes—
27C2×M16×D67C2212yes—
28#16864115C411yescharacteristic
29#16864110C411yescharacteristic
30#16864102C411yescharacteristic
31#16864091C412yes—
32#16864084C411yescharacteristic
33#16864082C412yes—
34#16864080C411yescharacteristic
35#16864074C412yes—
36#16864071C412yes—
37#16864048C411yescharacteristic
38#16864043C411yescharacteristic
39#16864039C411yescharacteristic
40#16863950C2211yescharacteristic
41#16863928C2211yescharacteristic
42#16863928C2212yes—
43#16863924C2212yes—
44#16863905C2212yes—
45C4×#11761629C2211yescharacteristic
46C4×#11761628C2211yescharacteristic
47C4×#11761628C2211yescharacteristic
48C4×D4×D67C2211yescharacteristic
49#117×D67C2212yes—
50#16863527C2211yescharacteristic, complemented
51#16863525C2212yescomplemented
52#16863524C2212yescomplemented
53#16863523C2211yescharacteristic, complemented
54#16863523C2212yescomplemented
55#16863523C2211yescharacteristic, complemented
56Q8×C67⋊C8C2211yescharacteristic, complemented
57C8×Dic134C2211yescharacteristic, complemented
58C8×Dic134C2212yescomplemented
59C8×Dic134C2211yescharacteristic, complemented
60#16863475C2211yescharacteristic
61#16863475C2211yescharacteristic
62#16863475C2212yescomplemented
63#16863474C2211yescharacteristic
64#16863473C2211yescharacteristic
65#16863473C2211yescharacteristic
66#16863473C2212yescomplemented
67#16863472C2212yes—
68#16863472C2212yescomplemented
69#16863472C2212yescomplemented
70#16863472C2212yescomplemented
71#16863471C2212yes—
72#16863470C2212yescomplemented
73#16863469C2212yescomplemented
74#16863468C2212yescomplemented
75#16863467C2212yes—
76#16863466C2212yescomplemented
77#16863464C2212yes—
78#16863464C2212yescomplemented
79#16863464C2212yescomplemented
80#16863464C2212yescomplemented
81D4×C67⋊C8C2211yescharacteristic
82D4×C67⋊C8C2212yescomplemented
83C8×C22⋊D67C2212yescomplemented
84#16863457C2212yescomplemented
85#16863455C2212yescomplemented
86#16863454C2212yescomplemented
87#16863454C2212yescomplemented
88#16863454C2212yescomplemented
89#16863453C2211yescharacteristic, complemented
90#16863452C2212yescomplemented
91#16863452C2211yescharacteristic, complemented
92#16863451C2212yescomplemented
93#16863448C2212yescomplemented
94#16863448C2211yescharacteristic, complemented
95#16863447C2212yescomplemented
96#16863421C2212yes—
97#16863421C2212yes—
98#16863418C2211yescharacteristic
99C4⋊C8×D67C2211yescharacteristic
100#16863361C2212yes—
101#16863358C2212yes—
102C22⋊C8×D67C2212yes—
103#16863354C2212yescomplemented
104#16863354C2211yescharacteristic, complemented
105#16863354C2211yescharacteristic, complemented
106#16863353C2211yescharacteristic
107#16863353C2211yescharacteristic
108#16863353C2212yes—
109#16863353C2211yescharacteristic, complemented
110#16863353C2211yescharacteristic, complemented
111#16863352C2212yescomplemented
112#16863351C2212yescomplemented
113#16863350C2212yes—
114#16863350C2212yes—
115#16863348C2212yescomplemented
116#16863348C2212yescomplemented
117C4×#11761611C2211yescharacteristic
118C4×#11761611C2212yescomplemented
119C4×#11761611C2211yescharacteristic, complemented
120C4×#11761611C2212yescomplemented
121C2×C4×C67⋊C8C2211yescharacteristic, complemented
122C4×C8×D67C2211yescharacteristic
123C4×C8×D67C2211yescharacteristic, complemented
124#529×C67C2211yescharacteristic
125#446×C67C2211yescharacteristic, complemented
126C8×Q8×C67C2211yescharacteristic, complemented
127#436×C67C2211yescharacteristic
128#436×C67C2212yescomplemented
129#435×C67C2212yescomplemented
130C8×D4×C67C2211yescharacteristic
131#433×C67C2212yescomplemented
132#431×C67C2211yescharacteristic, complemented
133#405×C67C2212yescomplemented
134C4×M16×C67C2211yescharacteristic, complemented
135C2×#11761629C2×C411yescharacteristic
136C2×#11761628C2×C411yescharacteristic
137C2×#11761628C2311yescharacteristic
138C2×D4×D67C2×C411yescharacteristic
139C22×C4×D67C2312yes—
140#14524051—24no—
141#14524051—24no—
142C2×#11761612C2312yes—
143C2×#11761611—28no—
144C2×#11761611C2311yescharacteristic
145C2×#11761611C2312yes—
146C2×#11761611C2312yes—
147C2×#11761611C2312yes—
148C2×#11761611C2311yescharacteristic
149C2×#11761611C2311yescharacteristic
150C2×#11761611C2312yes—
151C2×#11761611C2312yes—
152C2×#11761611C2311yescharacteristic
153M16×D67—28no—
154C22×C67⋊C8C2311yescharacteristic
155C22×C67⋊C8C2311yescharacteristic
156C22×C67⋊C8C2312yes—
157C2×C8×D67C2311yescharacteristic
158C2×C8×D67C2311yescharacteristic
159C2×C8×D67C2311yescharacteristic
160C2×C8×D67C2312yes—
161C2×C8×D67C2311yescharacteristic
162#14524042C2×C411yescharacteristic
163#14524041C2×C411yescharacteristic
164#14524038C2×C412yes—
165#14524036C2×C412yes—
166#14524036C2×C412yes—
167#14524036C2×C412yes—
168#14524036C2×C412yes—
169#14524034C2×C411yescharacteristic
170#14524034C2×C412yes—
171#14524033C2×C412yes—
172#14524033C2×C412yes—
173#14524030C2×C411yescharacteristic
174#14524030C2×C412yes—
175#14524029C2×C412yes—
176#14524028C2×C412yes—
177#14524028C2×C412yes—
178#14524025C2×C412yes—
179#14524025C2×C412yes—
180#14524025C2×C412yes—
181#14524025C2×C412yes—
182#14524025C2×C412yes—
183#14524023C2×C411yescharacteristic
184#14524023C2×C411yescharacteristic
185#14524023C2×C412yes—
186#14524021C2×C412yes—
187#14524021C2×C412yes—
188#14524021C2×C412yes—
189#14524020C2×C412yes—
190#14524019C2×C411yescharacteristic
191#14524016C2×C412yes—
192#14524016C2×C412yes—
193#14524015C2×C412yes—
194#14524014C2×C411yescharacteristic
195#14524014C2×C412yes—
196#14524013C2×C412yes—
197#14524011C2×C412yes—
198Q8×Dic67C2×C411yescharacteristic
199C4×Dic134C2×C411yescharacteristic
200C4×Dic134C2×C411yescharacteristic
201C4×Dic134C2×C411yescharacteristic
202C4×Dic134C2311yescharacteristic
203C4×Dic134C2312yes—
204C4×D268C2×C411yescharacteristic
205C4×D268C2×C411yescharacteristic
206C4×D268C2×C411yescharacteristic
207C4×D268C2311yescharacteristic
208C4×D268C2312yes—
209D4×Dic67C2×C411yescharacteristic
210#14524005C2×C411yescharacteristic
211#14524005C2×C411yescharacteristic
212#14524005C2×C412yes—
213C4×C22⋊D67C2×C411yescharacteristic
214C4×C22⋊D67C2×C411yescharacteristic
215C4×C22⋊D67C2×C411yescharacteristic
216C4×C22⋊D67C2×C412yes—
217C4×C22⋊D67C2×C411yescharacteristic
218C4×C22⋊D67C2312yes—
219C4×C22⋊D67C2312yes—
220C4×C22⋊D67C2312yes—
221(C22⋊D67)⋊C4C2×C412yes—
222#14524002C2×C411yescharacteristic
223#14524002C2312yes—
224#14524002C2311yescharacteristic
225#14524001C2×C412yes—
226#14524001C2×C412yes—
227#14524001C2×C412yes—
228#14524001C2×C411yescharacteristic
229#14524000C2×C412yes—
230#14524000C2311yescharacteristic
231#14524000C2312yes—
232#14524000C2311yescharacteristic
233#14523999C2×C412yes—
234#14523999C2×C412yes—
235C4⋊C4×D67C2×C412yes—
236C4⋊C4×D67C2×C411yescharacteristic
237C4⋊C4×D67C2×C412yes—
238C22⋊C4×D67C2×C412yes—
239C22⋊C4×D67C2×C412yes—
240C22⋊C4×D67C2×C412yes—
241C42×D67C2312yes—
242C42×D67C2312yes—
243C42×D67C2311yescharacteristic
244C42×D67C2311yescharacteristic
245C4⋊(C67⋊C8)C2311yescharacteristic
246C4⋊(C67⋊C8)C2311yescharacteristic
247C4⋊(C67⋊C8)C2312yes—
248C4⋊(C67⋊C8)C2312yes—
249Dic67⋊C8C2312yes—
250Dic67⋊C8C2312yes—
251Dic67⋊C8C2312yes—
252Dic67⋊C8C2312yes—
253Dic67⋊C8C2312yes—
254Dic67⋊C8C2312yes—
255C22⋊(C67⋊C8)C2312yes—
256C22⋊(C67⋊C8)C2312yes—
257C22⋊(C67⋊C8)C2312yes—
258(C2×D67)⋊C8C2312yes—
259(C2×D67)⋊C8C2312yes—
260(C2×D67)⋊C8C2312yes—
261(C2×D67)⋊C8C2312yes—
262(C2×D67)⋊C8C2312yes—
263(C2×D67)⋊C8C2312yes—
264#14523954C2312yes—
265#14523954C2312yes—
266#14523953C2311yescharacteristic
267#14523953C2312yes—
268#14523953C2312yes—
269#14523953C2311yescharacteristic
270#14523953C2311yescharacteristic
271#14523953C2312yes—
272#14523953C2311yescharacteristic
273C4×C67⋊C8C2311yescharacteristic
274C4×C67⋊C8C2312yes—
275C4×C67⋊C8C2311yescharacteristic
276C4×C67⋊C8C2311yescharacteristic
277C4×C67⋊C8C2311yescharacteristic
278C8×Dic67C2311yescharacteristic
279C8×Dic67C2312yes—
280C8×Dic67C2312yes—
281C8×Dic67C2311yescharacteristic
282C8×Dic67C2311yescharacteristic
283C8×Dic67C2311yescharacteristic
284C8×Dic67C2312yes—
285C2×M16×C67C2312yes—
286C2×M16×C67C2311yescharacteristic
287C2×M16×C67C2311yescharacteristic
288C22×C8×C67C2312yes—
289#126×C67C2×C412yes—
290#125×C67C2×C411yescharacteristic
291#124×C67C2×C411yescharacteristic
292#123×C67C2×C412yes—
293C22⋊Q8×C67C2×C411yescharacteristic
294#121×C67C2×C411yescharacteristic
295C4×Q8×C67C2311yescharacteristic
296C4×D4×C67C2311yescharacteristic
297C4×D4×C67C2312yes—
298#117×C67C2312yes—
299C2×C42×C67C2311yescharacteristic
300C4⋊C8×C67C2311yescharacteristic
301C4⋊C8×C67C2311yescharacteristic
302C4⋊C8×C67C2312yes—
303C4⋊C8×C67C2312yes—
304C22⋊C8×C67C2312yes—
305C22⋊C8×C67C2312yes—
306C22⋊C8×C67C2312yes—
307#97×C67C2312yes—
308#97×C67C2311yescharacteristic
309#97×C67C2311yescharacteristic
310C4×C8×C67C2311yescharacteristic
311C4×C8×C67C2311yescharacteristic
312C4×C8×C67C2312yes—
313C4×C8×C67C2312yes—
314C23×D67C22×C412yes—
315#11761629—42no—
316#11761628—22no—
317#11761628—22no—
318#11761628—42no—
319C2×Dic134C22×C411yescharacteristic
320C2×Dic134C22×C411yescharacteristic
321C2×Dic134C22×C412yes—
322C2×D268C22×C411yescharacteristic
323C2×D268C22×C411yescharacteristic
324C2×D268C22×C412yes—
325C2×C22⋊D67C22×C411yescharacteristic
326C2×C22⋊D67C22×C411yescharacteristic
327C2×C22⋊D67C22×C412yes—
328C2×C22⋊D67C22×C412yes—
329C2×C22⋊D67C22×C412yes—
330D4×D67—42no—
331C22×Dic67C22×C412yes—
332C2×C4×D67—24no—
333C2×C4×D67—24no—
334C2×C4×D67C22×C411yescharacteristic
335C2×C4×D67C22×C411yescharacteristic
336C2×C4×D67C22×C412yes—
337C2×C4×D67C22×C412yes—
338C2×C4×D67C22×C411yescharacteristic
339C2×C4×D67C22×C412yes—
340C2×C4×D67C22×C412yes—
341C2×C4×D67C22×C412yes—
342C2×C4×D67C22×C412yes—
343C2×C4×D67C22×C411yescharacteristic
344C2×C4×D67C2412yes—
345C2×C4×D67C2411yescharacteristic
346C2×C4×D67C2411yescharacteristic
347#11761612—24no—
348#11761611—24no—
349#11761611—22no—
350#11761611—24no—
351#11761611—24no—
352#11761611—22no—
353#11761611—24no—
354#11761611—24no—
355#11761611—22no—
356#11761611#4114yescomplemented
357C2×C67⋊C8—24no—
358C2×C67⋊C8—22no—
359C2×C67⋊C8—22no—
360C2×C67⋊C8C2411yescharacteristic
361C2×C67⋊C8C2412yes—
362C2×C67⋊C8C2412yes—
363C2×C67⋊C8C2411yescharacteristic
364C2×C67⋊C8C2411yescharacteristic
365C2×C67⋊C8C2411yescharacteristic
366C8×D67—24no—
367C8×D67—22no—
368C8×D67—22no—
369C8×D67—22no—
370C8×D67#4114yescomplemented
371C4⋊Dic67C22×C411yescharacteristic
372C4⋊Dic67C22×C412yes—
373C4⋊Dic67C22×C412yes—
374C4⋊Dic67C22×C412yes—
375C4⋊Dic67C22×C411yescharacteristic
376C4⋊Dic67C22×C411yescharacteristic
377C4⋊Dic67C22×C411yescharacteristic
378C4⋊Dic67C22×C412yes—
379Dic67⋊C4C22×C411yescharacteristic
380Dic67⋊C4C22×C411yescharacteristic
381Dic67⋊C4C22×C412yes—
382Dic67⋊C4C22×C412yes—
383Dic67⋊C4C22×C412yes—
384Dic67⋊C4C22×C412yes—
385Dic67⋊C4C22×C412yes—
386Dic67⋊C4C22×C411yescharacteristic
387Dic67⋊C4C22×C411yescharacteristic
388Dic67⋊C4C22×C412yes—
389Dic67⋊C4C22×C412yes—
390Dic67⋊C4C22×C412yes—
391C22⋊Dic67C22×C412yes—
392C22⋊Dic67C22×C412yes—
393C22⋊Dic67C22×C412yes—
394C22⋊Dic67C22×C412yes—
395C22⋊Dic67C22×C411yescharacteristic
396C22⋊Dic67C22×C411yescharacteristic
397C22⋊Dic67C22×C412yes—
398(C2×D67)⋊C4C22×C411yescharacteristic
399(C2×D67)⋊C4C22×C411yescharacteristic
400(C2×D67)⋊C4C22×C412yes—
401(C2×D67)⋊C4C22×C412yes—
402(C2×D67)⋊C4C22×C412yes—
403(C2×D67)⋊C4C22×C412yes—
404(C2×D67)⋊C4C22×C412yes—
405(C2×D67)⋊C4C22×C411yescharacteristic
406(C2×D67)⋊C4C22×C411yescharacteristic
407(C2×D67)⋊C4C22×C412yes—
408(C2×D67)⋊C4C22×C412yes—
409(C2×D67)⋊C4C22×C412yes—
410C4×Dic67C22×C412yes—
411C4×Dic67C22×C412yes—
412C4×Dic67C22×C412yes—
413C4×Dic67C22×C412yes—
414C4×Dic67C22×C411yescharacteristic
415C4×Dic67C22×C411yescharacteristic
416C4×Dic67C22×C411yescharacteristic
417C4×Dic67C22×C411yescharacteristic
418C4×Dic67C2411yescharacteristic
419C4×Dic67C2411yescharacteristic
420C4×Dic67C2412yes—
421C2×Q8×C67C22×C411yescharacteristic
422C2×D4×C67C22×C411yescharacteristic
423C2×D4×C67C22×C412yes—
424C22×C4×C67C22×C411yescharacteristic
425C22×C4×C67C22×C411yescharacteristic
426C22×C4×C67C2411yescharacteristic
427C22×C4×C67C2412yes—
428M16×C67—24no—
429M16×C67—22no—
430M16×C67—22no—
431C2×C8×C67—24no—
432C2×C8×C67C2412yes—
433C2×C8×C67C2412yes—
434C2×C8×C67C2411yescharacteristic
435C2×C8×C67C2411yescharacteristic
436C2×C8×C67C2411yescharacteristic
437C2×C8×C67C2411yescharacteristic
438C4⋊C4×C67C22×C412yes—
439C4⋊C4×C67C22×C412yes—
440C4⋊C4×C67C22×C411yescharacteristic
441C4⋊C4×C67C22×C412yes—
442C4⋊C4×C67C22×C411yescharacteristic
443C4⋊C4×C67C22×C412yes—
444C22⋊C4×C67C22×C412yes—
445C22⋊C4×C67C22×C412yes—
446C22⋊C4×C67C22×C412yes—
447C22⋊C4×C67C22×C412yes—
448C22⋊C4×C67C22×C412yes—
449C42×C67C22×C411yescharacteristic
450C42×C67C22×C411yescharacteristic
451C42×C67C2411yescharacteristic
452C42×C67C2412yes—
453C42×C67C2411yescharacteristic
454C23×C67C23×C412yes—
455C23×C67C23×C411yescharacteristic
456C22×D67—24no—
457C22×D67—42no—
458C22×D67—42no—
459C22×D67C23×C411yescharacteristic
460C22×D67C23×C412yes—
461C22×D67C23×C411yescharacteristic
462Q8×C67—22no—
463D4×C67—22no—
464D4×C67—42no—
465C2×C4×C67—22no—
466C2×C4×C67—22no—
467C2×C4×C67—21no—
468C2×C4×C67—21no—
469C2×C4×C67—22no—
470C2×C4×C67—41no—
471C2×C4×C67C23×C411yescharacteristic
472C2×C4×C67C23×C411yescharacteristic
473C2×C4×C67C23×C411yescharacteristic
474C2×C4×C67C23×C411yescharacteristic
475C2×C4×C67C23×C412yes—
476C2×C4×C67C23×C412yes—
477C2×C4×C67C23×C412yes—
478C2×C4×C67C23×C411yescharacteristic
479C2×C4×C67C2511yescharacteristic
480C22⋊D67—22no—
481C22⋊D67—22no—
482C22⋊D67—42no—
483C22⋊D67—42no—
484C22⋊D67—42no—
485C2×Dic67—24no—
486C2×Dic67C23×C412yes—
487C2×Dic67C23×C411yescharacteristic
488C2×Dic67C23×C411yescharacteristic
489C2×Dic67C23×C411yescharacteristic
490C2×Dic67C23×C411yescharacteristic
491C2×Dic67C23×C412yes—
492C2×Dic67C23×C412yes—
493C2×Dic67C23×C411yescharacteristic
494C2×Dic67C23×C411yescharacteristic
495D268—22no—
496D268—22no—
497D268—42no—
498C4×D67—24no—
499C4×D67—22no—
500C4×D67—22no—
501C4×D67—21no—
502C4×D67—21no—
503C4×D67—22no—
504C4×D67—22no—
505C4×D67—24no—
506C4×D67—41no—
507C4×D67—42no—
508C4×D67—42no—
509C4×D67—41no—
510C4×D67—42no—
511C4×D67—42no—
512C4×D67C2×#4112yes—
513C4×D67C2×#4112yes—
514Dic134—22no—
515Dic134—22no—
516Dic134—42no—
517C8×C67—22no—
518C8×C67—22no—
519C8×C67—21no—
520C8×C67—21no—
521C8×C67C2×#4112yes—
522C8×C67C2×#4112yes—
523C67⋊C8—21no—
524C67⋊C8—22no—
525C67⋊C8—22no—
526C67⋊C8—21no—
527C67⋊C8C2×#4112yes—
528C67⋊C8C2×#4112yes—
529C22×C67—22no—
530C22×C67—21no—
531C22×C67—21no—
532C22×C67—22no—
533C22×C67—22no—
534C22×C67—21no—
535C22×C67C24×C411yescharacteristic
536C2×D67—21no—
537C2×D67—21no—
538C2×D67—22no—
539C2×D67—21no—
540C2×D67—21no—
541C2×D67—22no—
542C2×D67—22no—
543C2×D67—21no—
544C2×D67—84no—
545C2×D67C4×#4112yes—
546C4×C67—21no—
547C4×C67—22no—
548C4×C67—21no—
549C4×C67—22no—
550C4×C67—22no—
551C4×C67—21no—
552C4×C67—21no—
553C4×C67#56812yes—
554C4×C67C22×#4111yescharacteristic
555C4×C67C22×#4111yescharacteristic
556Dic67—21no—
557Dic67—22no—
558Dic67—22no—
559Dic67—21no—
560Dic67—21no—
561Dic67—21no—
562Dic67—22no—
563Dic67—21no—
564Dic67C4×#4112yes—
565#60217—671nomaximal, Sylow
566C2×C67—42no—
567C2×C67—41no—
568C2×C67C2×C4×#4111yescharacteristic
569C2×C67C2×#56811yescharacteristic
570C2×C67#357311yescharacteristic
571D67—22no—
572D67—41no—
573D67—42no—
574#3475—671no—
575#2971—671no—
576#2971—671no—
577#2969—671no—
578#2969—672no—
579#2969—672no—
580#2969D6711yescharacteristic, complemented
581#2967—672no—
582#2967—672no—
583#2966—671no—
584#2966—671no—
585#2965—671no—
586#2965—671no—
587#2962—671no—
588#2960—671no—
589D4×M16—671no—
590#2933—672no—
591#2930—672no—
592C2×#436—671no—
593#2925—671no—
594#2924—672no—
595C4×#131—671no—
596#2873—672no—
597C67#6021711yescharacteristic, complemented, Sylow
598C2×#131—671no—
599C2×#131—671no—
600C22×M16—672no—
601C22×M16—672no—
602#556—671no—
603#555—671no—
604#554—671no—
605#553—672no—
606#552—672no—
607#552—671no—
608#552—671no—
609#551—672no—
610#551—672no—
611#547—671no—
612#546—671no—
613#546—671no—
614#533—671no—
615#529—671no—
616#529—672no—
617#529—672no—
618#529C2×D6711yescharacteristic
619#525—672no—
620C4×#41—671no—
621C4×#41—671no—
622C4×#41—671no—
623C2×C4×D4—671no—
624C2×#117—672no—
625#446—671no—
626#446—671no—
627#446—671no—
628#446—672no—
629#446—672no—
630#446—672no—
631#446C2×D6711yescharacteristic, complemented
632C8×Q8—671no—
633C8×Q8—672no—
634C8×Q8—671no—
635C8×Q8—671no—
636C8×Q8C2×D6711yescharacteristic, complemented
637#436—672no—
638#436—672no—
639#436—672no—
640#436—672no—
641#436—671no—
642#436—671no—
643#436—672no—
644#436—671no—
645#436—672no—
646#436—671no—
647#436—672no—
648#436—671no—
649#436C2×D6711yescharacteristic
650#436C2×D6712yescomplemented
651#435—672no—
652#435—672no—
653#435—672no—
654#435—672no—
655#435—672no—
656#435—672no—
657#435—672no—
658#435—672no—
659#435—672no—
660#435C2×D6712yescomplemented
661C8×D4—672no—
662C8×D4—672no—
663C8×D4—671no—
664C8×D4C2×D6711yescharacteristic
665#433—672no—
666#433—672no—
667#433—672no—
668#433—672no—
669#433—672no—
670#433C2×D6712yescomplemented
671#432—671no—
672#432—672no—
673#432—671no—
674#432—672no—
675#431—672no—
676#431—671no—
677#431—672no—
678#431C2×D6711yescharacteristic, complemented
679#424—672no—
680#424—672no—
681#423—671no—
682C2×C4⋊C8—671no—
683#408—672no—
684#407—672no—
685C2×C22⋊C8—672no—
686#405—672no—
687#405—671no—
688#405—671no—
689#405—672no—
690#405—672no—
691#405—671no—
692#405—672no—
693#405—671no—
694#405—671no—
695#405—671no—
696#405—672no—
697#405—672no—
698#405C2×D6712yescomplemented
699C4×M16—672no—
700C4×M16—672no—
701C4×M16—672no—
702C4×M16—672no—
703C4×M16—671no—
704C4×M16—671no—
705C4×M16C2×D6711yescharacteristic, complemented
706C2×C4×C8—671no—
707C2×C4×C8—671no—
708C2×C4×C8—671no—
709C2×#41—671no—
710C2×#41—671no—
711C2×#41—671no—
712C22×D4—671no—
713C23×C4—672no—
714#131—1344no—
715#131—1344no—
716C2×M16—672no—
717C2×M16—671no—
718C2×M16—672no—
719C2×M16—672no—
720C2×M16—672no—
721C2×M16—672no—
722C2×M16—672no—
723C2×M16—671no—
724C2×M16—671no—
725C2×M16—671no—
726C2×M16—1348no—
727C2×M16—1348no—
728C2×M16C22×D6712yes—
729C2×M16C22×D6711yescharacteristic
730C2×M16C22×D6711yescharacteristic
731C22×C8—671no—
732C22×C8—672no—
733C22×C8—671no—
734C22×C8—671no—
735C22×C8—672no—
736C22×C8—671no—
737C22×C8—671no—
738C22×C8—671no—
739C22×C8C22×D6712yes—
740C4⋊Q8—671no—
741C4⋊Q8—671no—
742#126—672no—
743#126—672no—
744#126—672no—
745#126—672no—
746#126—672no—
747#126C4×D6712yes—
748#125—672no—
749#125—672no—
750#125—671no—
751#125—672no—
752#125C4×D6711yescharacteristic
753#124—671no—
754#124—672no—
755#124—672no—
756#124C4×D6711yescharacteristic
757#123—672no—
758#123—672no—
759#123—672no—
760#123—672no—
761#123—672no—
762#123—672no—
763#123—672no—
764#123C4×D6712yes—
765C22⋊Q8—671no—
766C22⋊Q8—672no—
767C22⋊Q8—671no—
768C22⋊Q8—672no—
769C22⋊Q8—672no—
770C22⋊Q8—671no—
771C22⋊Q8—672no—
772C22⋊Q8—672no—
773C22⋊Q8C4×D6711yescharacteristic
774#121—672no—
775#121—672no—
776#121—671no—
777#121—672no—
778#121—672no—
779#121C4×D6711yescharacteristic
780#120—672no—
781#120—672no—
782C4×Q8—671no—
783C4×Q8—671no—
784C4×Q8—671no—
785C4×Q8—671no—
786C4×Q8—671no—
787C4×Q8—672no—
788C4×Q8C22×D6711yescharacteristic
789C4×D4—671no—
790C4×D4—671no—
791C4×D4—671no—
792C4×D4—671no—
793C4×D4—672no—
794C4×D4—671no—
795C4×D4—672no—
796C4×D4—672no—
797C4×D4—672no—
798C4×D4—671no—
799C4×D4—671no—
800C4×D4—672no—
801C4×D4—672no—
802C4×D4—671no—
803C4×D4—671no—
804C4×D4—671no—
805C4×D4—671no—
806C4×D4—672no—
807C4×D4C22×D6711yescharacteristic
808C4×D4C22×D6712yes—
809#117—671no—
810#117—672no—
811#117—671no—
812#117—672no—
813#117—672no—
814#117—672no—
815#117—671no—
816#117—672no—
817#117—672no—
818#117—672no—
819#117—671no—
820#117—672no—
821#117—671no—
822#117C22×D6712yes—
823C2×C4⋊C4—672no—
824C2×C4⋊C4—672no—
825C2×C4⋊C4—671no—
826C2×C22⋊C4—672no—
827C2×C22⋊C4—672no—
828C2×C22⋊C4—672no—
829C2×C42—672no—
830C2×C42—672no—
831C2×C42—671no—
832C2×C42—671no—
833C2×C42C22×D6711yescharacteristic
834C4⋊C8—672no—
835C4⋊C8—672no—
836C4⋊C8—672no—
837C4⋊C8—672no—
838C4⋊C8—672no—
839C4⋊C8—672no—
840C4⋊C8—671no—
841C4⋊C8—671no—
842C4⋊C8—672no—
843C4⋊C8—672no—
844C4⋊C8C22×D6711yescharacteristic
845C4⋊C8C22×D6711yescharacteristic
846C4⋊C8C22×D6712yes—
847C4⋊C8C22×D6712yes—
848C22⋊C8—672no—
849C22⋊C8—672no—
850C22⋊C8—672no—
851C22⋊C8—672no—
852C22⋊C8—672no—
853C22⋊C8—672no—
854C22⋊C8—672no—
855C22⋊C8—672no—
856C22⋊C8—672no—
857C22⋊C8C22×D6712yes—
858C22⋊C8C22×D6712yes—
859C22⋊C8C22×D6712yes—
860#97—671no—
861#97—671no—
862#97—672no—
863#97—671no—
864#97—672no—
865#97—672no—
866#97—671no—
867#97—672no—
868#97—672no—
869#97C22×D6711yescharacteristic
870#97C22×D6712yes—
871#97C22×D6711yescharacteristic
872C4×C8—671no—
873C4×C8—671no—
874C4×C8—671no—
875C4×C8—671no—
876C4×C8—672no—
877C4×C8—672no—
878C4×C8—672no—
879C4×C8—671no—
880C4×C8—671no—
881C4×C8—671no—
882C4×C8—671no—
883C4×C8—672no—
884C4×C8C22×D6711yescharacteristic
885C4×C8C22×D6711yescharacteristic
886C4×C8C22×D6712yes—
887C4×C8C22×D6712yes—
888C24—672no—
889#41—2682no—
890#41—2682no—
891#41—1342no—
892#41—1342no—
893C2×Q8—672no—
894C2×Q8—671no—
895C2×Q8—671no—
896C2×Q8C2×C4×D6711yescharacteristic
897C2×D4—2682no—
898C2×D4—672no—
899C2×D4—672no—
900C2×D4—672no—
901C2×D4—671no—
902C2×D4—671no—
903C2×D4—672no—
904C2×D4—671no—
905C2×D4—671no—
906C2×D4C2×C4×D6711yescharacteristic
907C2×D4C2×C4×D6712yes—
908C22×C4—671no—
909C22×C4—672no—
910C22×C4—672no—
911C22×C4—672no—
912C22×C4—672no—
913C22×C4—671no—
914C22×C4—671no—
915C22×C4—672no—
916C22×C4—671no—
917C22×C4—671no—
918C22×C4—672no—
919C22×C4—672no—
920C22×C4—672no—
921C22×C4—671no—
922C22×C4—1344no—
923C22×C4—1344no—
924C22×C4C2×C4×D6711yescharacteristic
925C22×C4C2×C4×D6711yescharacteristic
926C22×C4C23×D6711yescharacteristic
927C22×C4C23×D6712yes—
928M16—24no—
929M16—22no—
930M16—22no—
931M16—674no—
932M16—1344no—
933M16—1344no—
934M16—1342no—
935M16—1344no—
936M16—1342no—
937M16—1344no—
938M16—1344no—
939M16—1344no—
940M16—1342no—
941C2×C8—24no—
942C2×C8—671no—
943C2×C8—671no—
944C2×C8—674no—
945C2×C8—671no—
946C2×C8—672no—
947C2×C8—672no—
948C2×C8—671no—
949C2×C8—1342no—
950C2×C8—1344no—
951C2×C8—1342no—
952C2×C8—1344no—
953C2×C8—1342no—
954C2×C8—1342no—
955C2×C8—1342no—
956C2×C8C23×D6711yescharacteristic
957C2×C8C23×D6711yescharacteristic
958C2×C8C23×D6712yes—
959C2×C8C23×D6712yes—
960C2×C8C23×D6711yescharacteristic
961C2×C8C23×D6711yescharacteristic
962C4⋊C4—671no—
963C4⋊C4—671no—
964C4⋊C4—671no—
965C4⋊C4—672no—
966C4⋊C4—672no—
967C4⋊C4—672no—
968C4⋊C4—672no—
969C4⋊C4—672no—
970C4⋊C4—671no—
971C4⋊C4—671no—
972C4⋊C4—671no—
973C4⋊C4—672no—
974C4⋊C4—672no—
975C4⋊C4—672no—
976C4⋊C4—671no—
977C4⋊C4—671no—
978C4⋊C4—672no—
979C4⋊C4—672no—
980C4⋊C4—672no—
981C4⋊C4—672no—
982C4⋊C4C2×C4×D6712yes—
983C4⋊C4C2×C4×D6712yes—
984C4⋊C4C2×C4×D6711yescharacteristic
985C4⋊C4C2×C4×D6711yescharacteristic
986C4⋊C4C2×C4×D6712yes—
987C4⋊C4C2×C4×D6712yes—
988C22⋊C4—672no—
989C22⋊C4—672no—
990C22⋊C4—672no—
991C22⋊C4—671no—
992C22⋊C4—672no—
993C22⋊C4—671no—
994C22⋊C4—672no—
995C22⋊C4—671no—
996C22⋊C4—671no—
997C22⋊C4—672no—
998C22⋊C4—672no—
999C22⋊C4—672no—
1000C22⋊C4—672no—
1001C22⋊C4—672no—
1002C22⋊C4—672no—
1003C22⋊C4—671no—
1004C22⋊C4—672no—
1005C22⋊C4—671no—
1006C22⋊C4—672no—
1007C22⋊C4C2×C4×D6712yes—
1008C22⋊C4C2×C4×D6712yes—
1009C22⋊C4C2×C4×D6712yes—
1010C22⋊C4C2×C4×D6712yes—
1011C22⋊C4C2×C4×D6712yes—
1012C42—672no—
1013C42—672no—
1014C42—672no—
1015C42—672no—
1016C42—671no—
1017C42—671no—
1018C42—671no—
1019C42—671no—
1020C42—671no—
1021C42—671no—
1022C42—672no—
1023C42C2×C4×D6711yescharacteristic
1024C42C2×C4×D6711yescharacteristic
1025C42C23×D6711yescharacteristic
1026C42C23×D6711yescharacteristic
1027C42C23×D6712yes—
1028C23—2682no—
1029C23—2682no—
1030C23—671no—
1031C23—671no—
1032C23—672no—
1033C23—1344no—
1034C23C22×C4×D6712yes—
1035C23C22×C4×D6711yescharacteristic
1036Q8—22no—
1037Q8—2682no—
1038Q8—1342no—
1039Q8—1342no—
1040D4—22no—
1041D4—42no—
1042D4—2682no—
1043D4—2682no—
1044D4—2682no—
1045D4—2682no—
1046D4—1342no—
1047D4—1342no—
1048D4—1342no—
1049D4—1342no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—41no—
1056C2×C4—2682no—
1057C2×C4—2682no—
1058C2×C4—2681no—
1059C2×C4—2682no—
1060C2×C4—2681no—
1061C2×C4—2682no—
1062C2×C4—671no—
1063C2×C4—672no—
1064C2×C4—672no—
1065C2×C4—671no—
1066C2×C4—672no—
1067C2×C4—671no—
1068C2×C4—671no—
1069C2×C4—672no—
1070C2×C4—671no—
1071C2×C4—672no—
1072C2×C4—671no—
1073C2×C4—1344no—
1074C2×C4—1344no—
1075C2×C4—1344no—
1076C2×C4—1342no—
1077C2×C4—1342no—
1078C2×C4—1341no—
1079C2×C4—1341no—
1080C2×C4—1342no—
1081C2×C4—1342no—
1082C2×C4C22×C4×D6711yescharacteristic
1083C2×C4C22×C4×D6711yescharacteristic
1084C2×C4C22×C4×D6711yescharacteristic
1085C2×C4C22×C4×D6712yes—
1086C2×C4C22×C4×D6712yes—
1087C2×C4C22×C4×D6711yescharacteristic
1088C2×C4C22×C4×D6712yes—
1089C2×C4C22×C4×D6711yescharacteristic
1090C2×C4C24×D6711yescharacteristic
1091C8—22no—
1092C8—21no—
1093C8—22no—
1094C8—21no—
1095C8—672no—
1096C8—672no—
1097C8—1341no—
1098C8—1342no—
1099C8—1342no—
1100C8—1341no—
1101C8#41×D6712yes—
1102C8#41×D6712yes—
1103C22—21no—
1104C22—22no—
1105C22—22no—
1106C22—21no—
1107C22—21no—
1108C22—22no—
1109C22—5364no—
1110C22—672no—
1111C22—1342no—
1112C22—1341no—
1113C22—1342no—
1114C22—1341no—
1115C22—1342no—
1116C22—1341no—
1117C22—1341no—
1118C22—1341no—
1119C22C23×C4×D6711yescharacteristic
1120C4—21no—
1121C4—22no—
1122C4—22no—
1123C4—21no—
1124C4—21no—
1125C4—21no—
1126C4—22no—
1127C4—672no—
1128C4—1341no—
1129C4—1342no—
1130C4—1341no—
1131C4—1342no—
1132C4—1341no—
1133C4—1341no—
1134C4—1342no—
1135C4—1341no—
1136C4#1686416112yes—
1137C4C2×#41×D6711yescharacteristic
1138C4C2×#41×D6711yescharacteristic
1139C2—42no—
1140C2—41no—
1141C2—2682no—
1142C2—2681no—
1143C2—1342no—
1144C2C4×#41×D6711yescharacteristic
1145C2C2×#1686416111yescharacteristic
1146C2#2257492211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D67
commutator, socleC22×C67C24×C4
FittingC67×#2969C2
prime radical#22573765C2
cosocleC2×C4×C67C25
hypercenter#2969D67
hypocenterC67#60217
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #2969

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22569228C2semidirect
3. #22569227C2semidirect
4. #22569216C2semidirect
5. #22569216C2semidirect
6. #22569209C2semidirect
7. #22569192C2semidirect
8. #22569191C2semidirect
9. #22569185C2semidirect
10. #22569181C2semidirect
11. #22569174C2semidirect
12. #22569170C2semidirect
13. #22569157C2semidirect
14. #22569138C2semidirect
15. D4×#11761611C2semidirect
16. #22568935C2semidirect
17. #22568909C2semidirect
18. #436×D67C2semidirect
19. #22568870C2semidirect
20. #22568865C2semidirect
21. C4×#14524051C2semidirect
22. #22568625C2semidirect
23. C67×#2969C2semidirect
50. #16863527C22semidirect
51. #16863525C22semidirect
52. #16863524C22semidirect
53. #16863523C22semidirect
54. #16863523C22semidirect
55. #16863523C22semidirect
56. Q8×C67⋊C8C22semidirect
57. C8×Dic134C22semidirect
58. C8×Dic134C22semidirect
59. C8×Dic134C22semidirect
62. #16863475C22semidirect
66. #16863473C22semidirect
68. #16863472C22semidirect
69. #16863472C22semidirect
70. #16863472C22semidirect
72. #16863470C22semidirect
73. #16863469C22semidirect
74. #16863468C22semidirect
76. #16863466C22semidirect
78. #16863464C22semidirect
79. #16863464C22semidirect
80. #16863464C22semidirect
82. D4×C67⋊C8C22semidirect
83. C8×C22⋊D67C22semidirect
84. #16863457C22semidirect
85. #16863455C22semidirect
86. #16863454C22semidirect
87. #16863454C22semidirect
88. #16863454C22semidirect
89. #16863453C22semidirect
90. #16863452C22semidirect
91. #16863452C22semidirect
92. #16863451C22semidirect
93. #16863448C22semidirect
94. #16863448C22semidirect
95. #16863447C22semidirect
103. #16863354C22semidirect
104. #16863354C22semidirect
105. #16863354C22semidirect
109. #16863353C22semidirect
110. #16863353C22semidirect
111. #16863352C22semidirect
112. #16863351C22semidirect
115. #16863348C22semidirect
116. #16863348C22semidirect
118. C4×#11761611C22semidirect
119. C4×#11761611C22semidirect
120. C4×#11761611C22semidirect
121. C2×C4×C67⋊C8C22semidirect
123. C4×C8×D67C22semidirect
125. #446×C67C22semidirect
126. C8×Q8×C67C22semidirect
128. #436×C67C22semidirect
129. #435×C67C22semidirect
131. #433×C67C22semidirect
132. #431×C67C22semidirect
133. #405×C67C22semidirect
134. C4×M16×C67C22semidirect
356. #11761611#41semidirect
370. C8×D67#41semidirect
580. #2969D67semidirect
597. C67#60217semidirect
631. #446C2×D67semidirect
636. C8×Q8C2×D67semidirect
650. #436C2×D67semidirect
660. #435C2×D67semidirect
670. #433C2×D67semidirect
678. #431C2×D67semidirect
698. #405C2×D67semidirect
705. C4×M16C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225737652
#225692282
#225692272
#225692162
#225692092
#225691922
#225691912
#225691852
#225691812
#225691742
#225691702
#225691572
#225691382
D4×#117616112
#225689352
#225689092
#436×D672
#225688702
#225688652
C4×#145240512
#225686252
C67×#29692
#6021767